Incoherent thermal fluctuations of spins are critical in determining the magnetic properties of correlated systems. Thermally excited magnons drive various fundamental phenomena, including phase transitions and spin caloritronic effects. Their non-deterministic nature offers unique applications in probabilistic computing. Traditionally, incoherent spin fluctuations have been studied indirectly through macroscopic properties or in the frequency domain using optical probes like Raman scattering or diffraction. Spin noise spectroscopy (SNS) has been used for slower dynamics in paramagnets. However, antiferromagnets (AFMs), with their high-frequency magnons in the THz range, present a challenge for conventional SNS due to their ultrafast dynamics. Ultrafast pump-probe spectroscopy offers femtosecond time resolution, but it's perturbative and cannot detect spontaneous incoherent dynamics. This work experimentally demonstrates spontaneous incoherent sub-THz magnon fluctuation dynamics in an AFM using a novel femtosecond noise correlation spectroscopy technique inspired by sub-cycle quantum optics. This method analyzes magnon fluctuations via their temporal autocorrelation function by measuring the statistical correlations of polarization noise imprinted on two subsequent femtosecond probe pulses. The correlation of polarization changes induced by transient magnetization fluctuations via the Faraday effect is measured, revealing the time correlation trace of the out-of-plane sub-THz magnetization dynamics.

The study of spin fluctuations in magnetic materials has a long history, with early work focusing on indirect measurements through macroscopic properties such as heat capacity, conductivity, and magnetic susceptibility. More recently, advancements in optical techniques, including Raman spectroscopy and X-ray scattering, have enabled direct probing of spin fluctuations in the frequency domain. Spin noise spectroscopy (SNS), a powerful technique for studying relatively slow spin fluctuation dynamics in paramagnets, has emerged as a valuable tool. However, the ultrafast dynamics of antiferromagnets (AFMs) pose a significant challenge to conventional SNS methods. Ultrafast pump-probe spectroscopy, with its femtosecond time resolution, has been employed to investigate the rich spin physics in AFMs, particularly those with complex spin textures. However, the inherent perturbative nature of pump-probe techniques limits their ability to capture the spontaneous, incoherent dynamics driven by thermal or quantum fluctuations. This study bridges this gap by introducing a novel technique to directly measure spontaneous incoherent spin fluctuations in the sub-THz regime, providing a new perspective on the ultrafast dynamics in AFMs.

The experiment uses a mode-locked Er:fiber laser system generating 150 fs pulses at 1.55 µm, frequency-doubled to 775 nm for optimal transparency in the orthoferrite sample. The beam is split into two spectrally distinct probe pulses with a variable time delay (Δt). These pulses are focused onto a 10 µm thick c-cut Sm_0.7Er_0.3FeO₃ single crystal. Transient magnetization fluctuations induce polarization changes in the transmitted pulses via the Faraday effect. The polarization changes are measured using independent polarimetric detectors. Pulse-to-pulse fluctuations are extracted using sub-harmonic lock-in amplification, and the signals are multiplied and averaged over ~10⁶ pulses at each delay. This process yields the time correlation trace of the out-of-plane sub-THz magnetization dynamics. The volume scaling of the magnon noise is investigated by varying the sample position relative to the optical focus. The temperature dependence of the waveforms is studied around the spin reorientation transition (SRT). Fourier transforms of the autocorrelation waveforms are used to obtain the frequency spectra. Atomistic spin model simulations, based on the stochastic Landau-Lifshitz-Gilbert equation, are used to model the spin noise around the SRT. The simulations utilize a 192 x 192 x 192 orthoferrite spin lattice, incorporating nearest and next-nearest neighbor exchange interactions, Dzyaloshinskii-Moriya interaction, and various anisotropy terms to accurately reproduce the experimental observations. The simulations generate time traces of magnetization and corresponding spectral noise amplitude, which are then compared to the experimental results.

The study reveals spontaneous picosecond spin switching driven by thermal fluctuations in Sm_0.7Er_0.3FeO₃. A strong enhancement of magnon fluctuation amplitude and coherence time is observed around the SRT critical temperature. The frequency spectrum exhibits two distinct peaks: one corresponding to the quasi-ferromagnetic (qF) mode and a previously unreported low-frequency (LF) peak. The volume scaling of the noise amplitude follows the expected 1/Ω dependence, indicating the presence of mutually incoherent oscillators smaller than the probe spot size. The temperature dependence of the noise amplitude shows a sharp increase near the lower critical temperature of the SRT, followed by a decrease at higher temperatures. This is consistent with the rotation of the net magnetization during the SRT. Atomistic spin simulations reproduce the experimental observations, including the shape of the noise waveforms, temperature evolution of the amplitude, and the presence of two spectral peaks. The LF peak is identified as a signature of ultrafast random telegraph noise (RTN) resulting from picosecond random switching between two energetically degenerate quasi-equilibrium states created by the SRT. This switching behavior is clearly visualized in the simulated magnetization trajectories, where the system randomly flips between states with opposite magnetization, representing the fastest RTN ever reported. The simulations also show a qualitative agreement between the temperature dependence of the simulated qF mode fluctuations and the high-frequency experimental data, confirming the assignment of the high-frequency peak to the qF mode.

The discovery of ultrafast spontaneous spin switching in Sm_0.7Er_0.3FeO₃ driven by thermal fluctuations addresses the long-standing challenge of achieving picosecond switching in antiferromagnets without external perturbation. The observation of picosecond RTN represents a significant advancement in the field of stochastic magnetic systems, pushing the boundaries of speed for such devices. The close agreement between experimental results and atomistic spin simulations provides strong evidence for the proposed physical mechanism, linking the LF peak to the RTN dynamics. The results also highlight the importance of considering incoherent spin dynamics in THz magnonics in AFMs. This finding has important implications for probabilistic computing, where high-frequency RTN is crucial for faster computation and higher precision. The achieved switching speed is the fastest reported to date, surpassing previous nanosecond-scale RTN devices.

This work demonstrates the direct time-domain observation of sub-THz magnon fluctuations in Sm_0.7Er_0.3FeO₃ near the SRT, revealing ultrafast random spin switching as the origin of a previously unobserved low-frequency spectral feature. The observed picosecond RTN represents the fastest switching speed reported to date, suggesting potential applications in ultrafast probabilistic computing. The methodology developed in this study is broadly applicable to various correlated magnetic systems, opening new avenues for research in THz magnonics and the exploration of incoherent spin dynamics in equilibrium and non-equilibrium states.

The simulations, while successfully reproducing many aspects of the experimental observations, do not fully capture the complexity of the real material. Factors such as domain states and crystal defects are not explicitly included in the model, potentially leading to quantitative discrepancies between the simulations and experiments, especially regarding the precise temperature range of the SRT. The analysis of the frequency spectra relies on fitting with Lorentzian functions, which may not perfectly represent the complex spectral shapes. The limited time window of the measurements might affect the accuracy of the spectral analysis, particularly for the low-frequency components. The baseline correction procedure in the SRT region could potentially introduce some artefacts in the correlated spin noise data, although efforts were taken to mitigate this effect.